Про ефективні обчислення в підгрупах афінної напівгрупи Кремони та реалізаціях нових постквантових багатовимірних криптосистем: Fìz.-mat. model. ìnf. tehnol. 2021, 32:27-31

• Datum: 2021
• Hauptverfasser: Ustimenko, Vasyl, Pustovit, Oleksandr
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2021
• Schlagworte: постквантова криптографія; числова алгебра; множинна властивість композиції; підгрупи афінної групи Кремони; обчислювально ручний гомоморфізм; протоколи обміну ключами
• Online Zugang: https://www.fmmit.lviv.ua/index.php/fmmit/article/view/154
• Назва журналу: Physico-mathematical modeling and informational technologies

Multivariate cryptography (MC) together with Latice Based, Hash based, Code based and Superelliptic curves based Cryptographies form list of the main directions of Post Quantum Cryptography.Investigations in the framework of tender of National Institute of Standardisation Technology (the USA) indicates that the potential of classical MC working with nonlinear maps of bounded degree and without the usage of compositions of nonlinear transformation is very restricted. Only special case of Rainbow like Unbalanced Oil and Vinegar digital signatures is remaining for further consideration. The remaining public keys for encryption procedure are not of multivariate. nature. The paper presents large semigroups and groups of transformations of finite affine space of dimension n with the multiple composition property. In these semigroups the composition of n transformations is computable in polynomial time. Constructions of such families are given together with effectively computed homomorphisms between members of the family. These algebraic platforms allow us to define protocols for several generators of subsemigroup of affine Cremona semigroups with several outputs. Security of these protocols rests on the complexity of the word decomposition problem, Finally presented algebraic protocols expanded to cryptosystems of El Gamal type which is not a public key system. References Delaram, Kahrobaei, Bilal, Khan. (2006). A non-commutative generalization of ElGamal key exchange using polycyclic groups. In IEEE GLOBECOM 2006 - 2006 Global Telecommunications Conference [4150920]. DOI: 10.1109/GLOCOM.2006. DOI doi.org/10.1109/glocom.2006.290 Myasnikov, Alexei G., Shpilrain, Vladimir, Ushakov, Alexander. (2011). Non-commutative Cryptography and Complexity of Group-theoretic Problems. Amer. Math Soc. DOI doi.org/10.1090/surv/177 Roman'kov, V. (2019). An improved version of the AAG cryptographic protocol, Groups, Complex. Cryptol, 11(1), 35-42. Ben-Zvi, A., Kalka, A. Tsaban, B. (2018). Cryptanalysis via algebraic span, In: Shacham H. and Boldyreva A. (eds.) Advances in Cryptology – CRYPTO 2018 – 38th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 19-23, 2018, Proceedings, Part I, 10991, 255-274, Springer, Cham. DOI doi.org/10.1007/978-3-319-96884-1_9 Noether, Max, Cremona, Luigi. 1904. Mathematische Annalen 59, 1–19. Ustimenko, V. 2018. On new symbolic key exchange protocols and cryptosystems based on hidden tame homomorphism, Dopovidi. NAS of Ukraine, 10, 26-36. DOI doi.org/10.15407/dopovidi2018.10.026 Ustimenko, V. Klisowski, M. (2019). On Noncommutative Cryptography with cubical multivariate maps of predictable density, In “Intelligent Computing’’. Proceedings of the 2019 Computing Conference, Volume 2, Part of Advances in Intelligent Systems and Computing AISC, 99, 654-674. DOI doi.org/10.1007/978-3-030-22868-2_47 Ustimenko, V. (2019). On desynchronised multivariate algorithms of El Gamal type for stable semigroups of affine Cremona group. Theoretical and Applied Cybersecurity, National Technical University of Ukraine "Igor Sikorsky Kiev Polytechnic Institute" 1, 2019, 22-30. DOI doi.org/10.20535/tacs.2664-29132019.1.169022 Ustimenko, V. (2020). On the usage of postquantum protocols defined in terms of transformation semi-groups and their homomorphisma. Theoretical and Applied Cybersecurity, National Technical University of Ukraine "Igor Sikorsky Kiev Polytechnic Institute", 2, 32-44. DOI doi.org/10.20535/tacs.2664-29132020.1.209435